Details:
Title  A characterization of reduced forms of linear differential systems  Author(s)  Ainhoa AparicioMonforte, Elie Compoint, JacquesArthur Weil  Type  Article in Journal  Abstract  A differential system [ A ] : Y ′ = A Y , with A ∈ Mat ( n , k ¯ ) is said to be in reduced form if A ∈ g ( k ¯ ) where g is the Lie algebra of the differential Galois group G of [ A ] . In this article, we give a constructive criterion for a system to be in reduced form. When G is reductive and unimodular, the system [ A ] is in reduced form if and only if all of its invariants (rational solutions of appropriate symmetric powers) have constant coefficients (instead of rational functions). When G is nonreductive, we give a similar characterization via the semiinvariants of G . In the reductive case, we propose a decision procedure for putting the system into reduced form which, in turn, gives a constructive proof of the classical Kolchin–Kovacic reduction theorem.  ISSN  00224049 
URL 
http://www.sciencedirect.com/science/article/pii/S0022404912003404 
Language  English  Journal  Journal of Pure and Applied Algebra  Volume  217  Number  8  Pages  1504  1516  Year  2013  Edition  0  Translation 
No  Refereed 
No 
